© 2019 IEEE. Accepted Version. Published version at DOI: 10.1109/TIA.2019.2911057 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new

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Real-Time Control of a Full Scale Li-ion Battery and Li-ion Capacitor Hybrid Energy Storage System for a Plug-in Hybrid Vehicle

Phillip J. Kollmeyer1, Mackenzie Wootton1, John Reimers1, Daniel F. Opila2, Himesh Kurera1, Mrudang Kadakia1, Ran Gu1, Tyler Stiene1, Ephrem Chemali1, Megan Wood1, Ali Emadi1

1McMaster University Electrical and Computer Engineering Department

Hamilton, ON, Canada Corresponding email: kollmeyp@mcmaster.ca

2United States Naval Academy Electrical and Computer Engineering Department

Annapolis, MD

Abstract - A semi-active hybrid energy storage system, consisting of a Li-ion battery pack, dc/dc converter, and Li-ion capacitor pack was developed for a range extended plug-in vehicle. The vehicle has a series-parallel drivetrain with two electric motors, a gas engine, gearbox, and a clutch to allow the engine to run decoupled from the gearbox in range extending mode. The peak dc electrical requirement of the electric drivetrain is about 175kW, which is similar to the peak power capability of the developed hybrid energy storage system. A model of the prototype hybrid energy storage system, which has the Li-ion capacitor pack connected directly to the motor drive’s dc bus and the battery pack connected to the Li-ion capacitor pack via a dc/dc converter, is developed and used to determine the optimal power split between the battery and Li-ion capacitor packs and for tuning the developed real-time control system. The real-time control system is shown through modeling and experimental testing of the full scale HESS to reduce battery pack losses, increase vehicle range, and to have performance approaching that of the optimal control solution as calculated via dynamic programming.

Index Terms - hybrid energy storage system, Li-ion battery, Li-ion capacitor, real-time control, dynamic programming

I. INTRODUCTION Plug-in hybrid electric vehicles (PHEVs) utilize battery

packs which must provide the drivetrain peak power as well as the energy to drive between 20 and 80 km in charge depleting (electric only) mode. As a result, a typical light duty PHEV battery pack has five to fifteen kWh of energy storage and a power requirement of 60 to 100kW, requiring the use of a high power to energy ratio battery. These batteries tend to have lower energy density, may require significant cooling, and may not be sufficient for high performance applications. As an alternative, hybrid energy storage systems (HESSes) consisting of a power dense and an energy dense storage device have been considered for many electrified vehicle applications [1-10]. Several studies have looked specifically at HESS’s for electric vehicles and shown significant range improvements [1-3]. Many combinations of energy storage devices have been investigated for electric vehicles, including a Li-ion capacitor and NaS battery [1], a Li-ion capacitor and lead-acid battery pack [2], and an ultracapacitor and Li-ion battery pack [3-4]. HESS performance has also been modeled for hybrid electric vehicle applications [5-8], including the work preceding this study [9]. This paper provides a contribution significantly beyond that in [9] by including the development of a real-time controller, benchmarking the real-time controller against the optimal control solution, and by validating the system model and real-time controller with testing of the full-scale HESS.

The development of a HESS for a PHEV with a higher than typical power requirement – a prototype plug-in Chevrolet Camaro – is investigated in this study. The electrified Camaro, referred to as the E28, is McMaster University’s vehicle for the US Department of Energy sponsored EcoCAR3 competition. The Camaro is what is colloquially referred to as a “muscle car”, and is therefore expected to be a high-performance vehicle, with gas powered versions supplying between 200kW and 340kW of power. The prototype hybrid version was therefore designed to compete with the gas version and has 150kW of electric traction power and a total of 350kW of power with the gas engine operating. A HESS was chosen to allow the use of a smaller (10.9kWh), high energy density battery pack for this high-power application.

The developed HESS utilizes a semi-active topology, which is defined as a topology with a single dc/dc converter which provides direct control of the power flow of one of the two energy storage devices. For this semi-active topology, the Li-ion capacitor is connected to the inverter dc bus and the battery pack is connected via a dc/dc converter. This HESS topology was chosen to maximize the current filtering capability of the Li-ion capacitors [10], while reducing the battery pack voltage and dc/dc converter power requirements [10]. While this topology would typically require a larger power pack because the DC bus voltage is not able to vary as much, Li-ion doped capacitors, which have two to four times the energy density of typical carbon ultracapacitors [11], are utilized to minimize the difference in pack sizing.

The performance which can be achieved with the developed HESS depends heavily on how the power flow is split between the battery and Li-ion capacitor pack. In prior art, dynamic programming (DP), an optimization methodology, has been utilized to determine the HESS power split which will minimize battery rms current [12], battery aging [5], and total energy storage system loss [3]. DP is utilized in this paper to determine the optimal power split for the proposed HESS, with the goals of minimizing energy storage system loss, maximizing regenerative braking energy capture, and minimizing motor power limiting. A real-time controller is then developed and benchmarked against the optimal control solution.

Many different real-time control methods have been proposed in prior research, such as a strategy to minimize electric traction system losses via management of the dc bus voltage [4], a method which sets the ultracapacitor voltage target as a function of vehicle speed [13], and a variety of other methods in over twenty additional studies outlined in [14]. The real-time control developed in this work uses an optimal control derivation to determine the structure of optimal solutions, but is implemented with only two tunable parameters. Compared to other methods, this technique requires no direct future This project has been supported by the Canadian Excellence Research

Chair in Hybrid Powertrain and the EcoCAR3 competition

© 2019 IEEE. Accepted Version. Published version at DOI: 10.1109/TIA.2019.2911057 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new

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predictions, is simple to implement and relatively insensitive to modeling errors, yet can still produce near-optimal performance. The controller aims to minimize system loss while respecting power, charge, and voltage constraints. This controller structure was derived in [15] to minimize battery degradation, but here is instead used to maximize range. The developed real-time controller is implemented on the full-scale prototype HESS and tested with an aggressive vehicle drive cycle to demonstrate the accuracy of the proposed modeling methodology and the performance which can be achieved in a real system.

II. VEHICLE DRIVETRAIN DESIGN AND MODELING To evaluate the performance of the HESS in the vehicle, a

drivetrain model from which the HESS power can be calculated for a given drive cycle is required. The drivetrain design and corresponding model are presented in the following subsections.

A. Vehicle drivetrain design The E28 plug-in hybrid electric vehicle is shown in Fig. 1

and the corresponding series-parallel vehicle architecture is shown in Fig. 3. Two three phase motor drives (Rinehart Motion Systems PM150DZR) are utilized and paired with axial flux permanent magnet machines (Yasa Motors P400), which can individually supply up to 325Nm and about 75kW with the available phase current and bus voltage. To allow the system to operate in four distinct modes, the drivetrain also has a clutch as is shown in Fig. 3. In electric only mode, this allows the system to utilize either one or both electric machines, giving a peak electric mode power of 75kW or 150kW. More details regarding range extending mode can be found in [9]. The HESS, as shown in Fig. 2 and illustrated in Fig. 3, must provide all the traction system energy and power in electric only mode. This charge depleting mode, being the most demanding HESS operating state, is therefore the focus of this paper.

B. Vehicle drivetrain modeling A vehicle model including drivetrain component losses,

mechanical drag, and acceleration forces was developed and is used to determine the HESS power requirements, PHESS, for the

Fig. 1 McMaster EcoCAR3 Team’s E28 series-parallel plug-in hybrid electric

2016 Chevrolet Camaro

Fig. 2 Battery / Li-ion capacitor hybrid energy storage system in trunk of

vehicle

Fig. 3 E28 series-parallel powertrain and HESS block diagram

investigated drive cycles. The mechanical parameters for the vehicle model, including the vehicle mass, assumed driver and cargo mass, tire radius, and the coast down or road load parameters, are provided in Table I. Additionally, a gearbox efficiency of 98%, differential efficiency of 96%, and electrical accessory power of 500W is assumed. The motor and drive loss modeling and the equations for calculating the total drivetrain power are detailed in [9].

To give insight into how much energy and power is required to propel the vehicle at a constant speed, the model calculated road load power and constant speed energy consumption are shown in Fig. 4. Fig. 4 (a) shows that 20kW of mechanical power are needed to propel the vehicle at 100km/h and Fig. 4 (b) shows that at this speed about 21kWh/100km is required from the HESS. For the 10.9kWh battery pack in the vehicle, this would translate to about 50km of all electric range at 100km/h, and significantly less range at higher speeds.

TABLE I. VEHICLE MODEL PARAMETERS AND ASSUMPTIONS Mass of modified vehicle 1938kg a (with fuel tank full)

Driver & Cargo Mass 100kg b

Coast down / road load coefficients

A B C 177N c 6.04N/(m/s) c 0.45N/(m/s2) c

Tire Radius 0.34 m Gearbox Efficiency 98%b

Differential Efficiency 96% b Electrical Accessory

Power 500Wb

a. Measured with vehicle corner weights, b. Assumptions, c. Parameters from [16]

(a) Road load power (b) Constant speed energy consumption

Fig. 4 Model predicted constant speed road load power and HESS energy consumption

© 2019 IEEE. Accepted Version. Published version at DOI: 10.1109/TIA.2019.2911057 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new

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(a) Prototype battery pack with

enclosure (b) Prototype Li-ion capacitor pack

with enclosure removed

(c) Brusa dc/dc converter

Fig. 5 Hybrid energy storage system components

III. HYBRID ENERGY STORAGE SYSTEM DESIGN & EXPERIMENTAL CHARACTERIZATION

A. Hybrid Energy Storage System Design and Prototype The hybrid energy storage system components (Fig. 5)

consist of a battery pack connected to a Li-ion capacitor pack via a 400A rated dc/dc converter (Brusa BDC546), as is illustrated in Fig. 2. The dc/dc converter has a non-isolated multiphase buck / boost topology, which does not allow for the low and high side voltage to cross over. The voltage of the battery pack, which is connected to the low side, must therefore be less than that of the Li-ion capacitor pack, which is connected to the high side. The battery pack and Li-ion capacitor packs were designed with these limitations in mind, and with the goal of having the HESS be able to provide at least 175kW of power. To help attain the highest possible energy density for the system, an LG Chem 18650 HG2 battery cell was selected for

Table II. BATTERY CELL / PACK PARAMETERS Make / Model LG HG2 18650 NMC

# of series cells / parallel 84s12p Amp-hours per cell / pack 3Ah / 36Ah Nominal Voltage/Energy 302V (3.6V/cell) / 10.9kWh

Voltage Range 210 - 353V (2.5 - 4.2V/cell) Bus Bar Resistance 19mΩ a Nominal Resistance 28mΩ (cell) a / 215mΩ (pack) a Pack Current Limit 400A peak b

Total Cell Mass / Volume 47.4 kg / 17.2 L Total PCM Mass 15.1kg

Total Pack Mass / Volume 90.3 kg / 84.0 L

a. From experimental testing, b. Limited by dc/dc converter

TABLE III. LI-ION CAPACITOR CELL / PACK PARAMETERS Make /Model JM Energy CP3300S

# of series cells 108 Farads per cell 3300F

Nominal Energy 4.4Wh (cell) / 475Wh (pack) Voltage Range 238-410V (2.2-3.8V/cell)

Bus Bar Resistance 8mΩ a

Nominal Resistance 1mΩ (cell)b / 126mΩ (pack)c 1.2mΩ (cell)a / 138mΩ (pack)a

Pack Current Limit 360A Total Cell Mass / Volume Approx. 39.9 kg / 23.9 liters

Total Pack Mass / Volume 90.7 kg / 124.2 liters a. From experimental testing, b. From cell datasheet, c. Scaled from 12 cell module datasheet

the battery pack. This 3 amp-hour (Ah) nickel manganese cobalt (NMC) chemistry cell has an energy density of 230Wh/kg and is rated for up to 20A continuous discharge current. A total of 1008 cells are utilized, in an 84 series 12 parallel (84s12p) configuration, providing 10.9kWh of energy storage with just 47.4kg of cells, as specified in Table II. The battery cells are also packaged in a total of 15kg of a phase change material (PCM) for thermal management. The material has a high heat capacity in the region in which the PCM changes phase, from 48 to 57°C, reducing the battery’s temperature rise during operation and protecting against thermal runaway and failure propagation.

For the Li-ion capacitor pack, as shown in Fig. 5 (b), Li-ion capacitors from JM Energy were chosen because their gravimetric and volumetric energy density (13Wh/kg and 20Wh/L) are about double that of conventional ultracapacitors (7Wh/kg and 9Wh/l) [11]. The pack was designed with a total of 108 series connected 3300F Li-ion capacitor cells, providing 475Wh of total energy as specified in Table III. The Li-ion capacitors have less total mass (39.9kg) than the battery cells (47.4kg), but more volume (23.9L vs 17.2L). Importantly the Li-ion capacitor pack has less resistance than the battery pack and as a result has higher power capability.

B. Experimental Testing and Modeling of HESS Components The HESS components were modeled using experimentally

derived data, ensuring the highest level of accuracy for the HESS model. Individual battery and Li-ion capacitor cells were first tested using an automated battery test system. Then the battery pack, capacitor pack and HESS DC/DC converter were tested in situ by modifying the vehicle’s control logic and instrumenting the HESS with a Yokogawa WT1800 power analyzer and two external LEM Ultrastab 867 current transducers.

1) DC/DC Converter Testing The Brusa BDC546 dc/dc converter achieves a very high

level of efficiency, up to 99%, by utilizing a non-isolated eight phase buck / boost resonant topology with zero current switching [17]. The converter loss was measured for a range of buck and boost mode currents, as shown in Fig. 6 (a). The loss was measured with a high-side (Li-ion capacitor pack) voltage of about 400V, and with a low-side (battery pack) voltage of 260 to 300V. The measured loss ranged from around 400W at 100A of low side current to 1000W at 250A, and is extrapolated to 2300W of loss at 400A.

These loss values translate to efficiency ranging from 97 to 98.9% for currents greater than 50A, as is shown in Fig. 6 (b) for a battery pack voltage of 210V and 350V. This high

(a) Measured dc/dc converter losses

with high side voltage ≈ 400V (b) DC/DC efficiency calculated from measured loss for two battery voltages

Fig. 6 Experimental DC/DC converter loss and efficiency

© 2019 IEEE. Accepted Version. Published version at DOI: 10.1109/TIA.2019.2911057 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new

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efficiency is especially impressive considering that the converter is being utilized at less than its intended voltage (up to 750Vdc), and means that the dc/dc converter loss will have relatively little impact on the total HESS efficiency. The dc/dc converter loss is modeled simply as a current dependent loss, as shown by the 2nd order polynomial fit curve in Fig. 6 (a). The converter loss will also vary somewhat with Li-ion capacitor voltage, but this variance has been neglected in the modeling.

2) Battery and Li-ion capacitor cell testing and modeling

An LG HG2 battery cell and CP3300S Li-ion capacitor cell underwent testing at 25°C using a high accuracy automated battery cycler and a thermal chamber. The LG HG2 cell was tested with a standard hybrid pulsed power characterization (HPPC) test with ten-second long current pulses, a discharge current magnitude of 12.5A, and a charge current of 3A. The resulting open circuit voltage (OCV) and charge and discharge resistances for this test are shown in Fig. 7. The cell resistance is around 28mΩ until about 30% state of charge (SOC), where the resistance starts to rise rapidly. The values are also scaled for the full 84s12p pack, showing open circuit voltage ranging from 240 to 350V and resistance ranging from 200 to 400mΩ.

The Li-ion capacitor cell was tested with a 5A constant current discharge to determine the approximate OCV versus amp-hours curve, as shown in Fig. 8 (a). The capacitance was then calculated from the voltage and amp-hour measurement for each set of voltage points using the definition of capacitance, Q = CV, and the resulting capacitance versus OCV characteristic is given in Fig. 8 (b). The capacitance is shown to vary by about 20% with respect to voltage, a significant enough variance that it is important to include in the modeling. Additionally, the Li-ion capacitor resistance was measured by applying a 10A current pulse and measuring the difference between the OCV and the voltage under load. The measured resistance values are shown to vary from 1.2 to 1.35mΩ in Fig. 8 (b).

(a) Measured battery cell OCV, scaled

for 84s12p pack (b) Measured battery cell resistance,

scaled for 84s12p pack Fig. 7 LG HG2 cell parameters experimentally measured at 25°C

(a) Measured cell voltage versus state

of charge (b) Measured cell capacitance and

resistance Fig. 8 JM Energy CP3300s Li-ion capacitor cell parameters experimentally

measured at 25°C

(a) Battery model (b) Li-ion capacitor model

Fig. 9 Battery and Li-ion capacitor equivalent circuit models

(a) Battery pack with 50A current

pulse (b) Li-ion capacitor pack with 15A

current pulse Fig. 10 Bus bar resistance determined from comparison of pack and

individual cell measurements

The parameters in Fig. 7 and Fig. 8 are then used to model the battery and Li-ion capacitor cell performance with the simple models presented in Fig. 9. The battery parameters are a function of the amp-hours (Ah) discharged from the cell, and the Li-ion capacitor parameters are a function of OCV (Vc). These simple models are sufficient for estimating the battery and Li-ion capacitor performance and loss at room temperature, but more sophisticated temperature dependent models as presented in [3] would be necessary to extend the modeling to low temperatures.

3) Li-ion capacitor cell and pack testing The battery and capacitor pack OCV and discharge

resistance curves were extrapolated from the respective cell testing results in Fig. 7 and Fig. 8. This extrapolation does not account for the pack bus bar and cabling resistance though, so a pulse current was applied to the pack and compared to cell testing to determine the pack bus bar resistances. A bus bar resistance of 19mΩ was observed for the battery pack and 8mΩ for the Li-ion capacitor pack, as is illustrated in Fig. 10.

C. Battery Pack, Capacitor Pack and HESS Power Capability The HESS’s power capability is a function of the battery

pack and Li-ion capacitor pack power capability and the dc/dc converter current rating. The battery pack charge and discharge power capability is calculated, considering cell voltage and current limits, to be as high as 20kW and 100kW respectively as shown in Fig. 11 (a). Due to its lower resistance the Li-ion capacitor pack charge and discharge power capability is higher, greater than 100kW over most of the SOC range. The total HESS discharge power capability envelope, which is limited by the requirement that Li-ion capacitor pack voltage be higher than the battery pack voltage, is shown in Fig. 11 (b). The power capability exceeds 175kW over much of the battery SOC range, showing the HESS meets the vehicle’s peak power requirement.

© 2019 IEEE. Accepted Version. Published version at DOI: 10.1109/TIA.2019.2911057 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new

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(a) Battery pack power capability (b) HESS discharge power capability

for a range of battery SOC and Li-ion capacitor OCV values

Fig. 11 Battery pack and total HESS power capabilities calculated from experimental parameters

IV. OPTIMAL POWERSPLIT FOR THE HESS The power split is the ratio of power provided by the battery

and Li-ion capacitor packs. The optimal power split is defined as the power split that minimizes the net charge, or amp-hours, drawn from the battery during a drive cycle, which in effect (1) minimizes the total HESS losses and (2) maximizes regenerative braking energy capture. The optimal power split for a drive cycle is determined using a dynamic programming (DP) function [18] whose application to a HESS is described more fully in [14]. The DP function is set up with Li-ion capacitor voltage as the single state variable, battery current as the control function, solution grids of 400 points, system voltage and current limits as defined in the prior section, and with the cost trajectory set to the optimization goals, as is described in TABLE IV.

The DP formulation includes constraints such that (1) the commanded motoring power is always provided, and (2) the Li-ion capacitor terminal voltage is at least 10V higher than battery terminal voltage to prevent uncontrolled rectification with the dc/dc converter. Rather than having battery SOC as a second state variable, the battery trajectory was precalculated assuming all power was provided by the battery, and the DP algorithm was iteratively run with updated battery SOC values. This method was observed to result in the proper optimal solution because battery SOC is not strongly effected by the power split. Importantly, for DP the full drive cycle must be known ahead of time, so the presented results represent the best-case performance for a causal control system.

TABLE IV. DYNAMIC PROGRAMMING SPECIFICATIONS USING

NOMENCLATURE PROVIDED IN [18] Variable Variable Specifications

Control function U Battery Current

Minimum: - 48A (battery charge limit) Maximum: + 400A (dc/dc current limit) # of points in grid: 400

Cost function C Value to minimize via

selection of control function trajectory

C = ∑𝐼𝐼𝑏𝑏 , minimizes net Ah drawn from battery, has effect of: (1) Minimizing sum of HESS losses (2) Maximizing regenerative braking energy

capture

State variable X Li-ion capacitor Voltage

Minimum: 238V Maximum: 400V # of points in grid: 400

Other voltage limits Limit: Li-ion capacitor voltage must be at least 10V greater than battery voltage to ensure dc/dc converter low side voltage (battery) does not exceed high side voltage (Li-ion capacitor)

(a) Battery voltage

(b) Battery current

Fig. 12 Modeled battery performance for US06 drive cycle battery only and HESS cases with DP control

TABLE V. US06 BATTERY ONLY & HESS PERFORMANCE FOR DP CONTROL Battery Only HESS Difference

Range (approx.) 30.2km 38.4km +27% / +8.2km Regen Energy Capture 32 Wh/km 66Wh/km +110%

Battery Loss 48 Wh/km 17 Wh/km -64% Li-ion capacitor Loss - 5.5 Wh/km -

DC/DC Converter Loss - 4.6 Wh/km - Total ESS Loss 48 Wh/km 27 Wh/km -43%

Fig. 13 Modeled range and regenerative braking energy capture improvement

achieved with DP control for four drive cycles

To give an indication of how well the HESS performs, the HESS is compared to the alternative of using just the battery pack (battery only case) for the US06 drive cycle in Fig. 12. The model repeats the drive cycle until the battery state of charge is 10% for the battery only case, and then determines the optimal power split for the HESS case. Fig. 12 shows that with the HESS battery current is smoothed significantly. Overall, with the HESS for the US06 drive cycle the vehicle range is increased by 27% (8.2km). This improvement is due to a more than 100% increase in regenerative braking energy capture, a 64% reduction in battery loss, and a 43% reduction in total energy storage system loss, as detailed in TABLE V.

The battery only and HESS performance was also modeled for the highway (HWFET), urban (UDDS), and more aggressive LA92 drive cycles, and an increase in vehicle range of 6, 11, and 29% was predicted respectively, as is shown in Fig. 13. The increase in range is due primarily to a 20 to 110% increase in

© 2019 IEEE. Accepted Version. Published version at DOI: 10.1109/TIA.2019.2911057 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new

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regenerative braking energy, as is also shown in Fig. 13, as well as due to a reduction in total energy storage system loss. Regenerative braking energy capture was increased because of the high charge capability, around 100kW, of the Li-ion capacitor pack. The battery pack, for comparison, has a charge capability of just 20kW, limiting the braking energy which can be captured for the battery only case. The low resistance of the Li-ion capacitor pack results in the reduction of the battery pack and overall system loss.

V. REAL-TIME HESS CONTROLLER

A. Control Theory A complete optimal solution requires exact future

knowledge of the system dynamics and drive cycle, as was computed for the DP solution. Future driving behavior is not exactly known, so for real-time implementation a controller is used that approximates characteristics of the optimal solution using only two tunable parameters without explicit future knowledge of the trip. This controller was originally proposed in [15] for minimizing battery degradation, but here is used to minimize losses only, without considering degradation.

The derivation of this real-time controller makes several simplifying model assumptions, but the final implementation uses the full models discussed in previous sections. Namely,

1) The battery and capacitor power limits may be neglected. 2) The system cost (loss) is additive over time. 3) The battery and dc-dc converter losses depend on battery SOC,

but the SOC trajectory over the cycle is not significantly changed by the HESS operation (e.g. the Li-ion capacitor capacity is far less than the battery). Thus it is considered an exogenous input evolving via the cycle power demand PHESS.

4) The capacitor is treated as an ideal storage element with a separate loss function that depends only on power output.

The system cost at each instant is the total system losses, as

𝐶𝐶(𝑃𝑃𝐶𝐶 , 𝑆𝑆𝑆𝑆𝐶𝐶𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏) = 𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙−𝐶𝐶(𝑃𝑃𝐶𝐶)+ 𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙−𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑(𝑃𝑃𝐶𝐶 , 𝑆𝑆𝑆𝑆𝐶𝐶𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏)+ 𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙−𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏(𝑃𝑃𝐶𝐶 , 𝑆𝑆𝑆𝑆𝐶𝐶𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏)

(1)

where the cost C is the total HESS loss, PC is Li-ion capacitor output power, and Ploss-C, Ploss-dcdc, and Ploss-batt are the Li-ion capacitor, dc/dc converter, and battery loss respectively. The Li-ion capacitor and battery loss are calculated from their measured resistance and calculated current for the respective operating point, and the dc/dc converter loss is calculated as a function of battery current using the loss characteristic in Fig. 6 (a).

In discrete time this results in the optimization problem

min𝑃𝑃𝐶𝐶

𝐶𝐶𝑘𝑘𝑃𝑃𝐶𝐶𝑘𝑘 , 𝑆𝑆𝑆𝑆𝐶𝐶𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑇𝑇

0

such that

(2)

𝑃𝑃𝑑𝑑𝑘𝑘

𝑇𝑇

0

= 0 (3)

where the constraint (3) is added to reflect that the capacitor is storage only and cannot be a net provider of energy. Using Lagrange multipliers (see [15] for full details), for an optimal solution 𝑃𝑃𝐶𝐶 , the first order necessary conditions are

𝜕𝜕ℒ𝜕𝜕𝜆𝜆

= 0 = 𝑃𝑃𝐶𝐶𝑘𝑘

𝑇𝑇

0

(4)

𝜕𝜕ℒ𝜕𝜕𝑃𝑃𝐶𝐶𝑘𝑘

= 0 =𝜕𝜕𝐶𝐶𝑘𝑘𝑃𝑃𝐶𝐶𝑘𝑘 , 𝑆𝑆𝑆𝑆𝐶𝐶𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏

𝜕𝜕𝑃𝑃𝐶𝐶𝑘𝑘+ 𝜆𝜆 (5)

and the Lagrangian (the cost (1) plus 𝜆𝜆 times the constrant (3)) will have a local minimum with respect to 𝑃𝑃𝐶𝐶 . The Lagrangian is a sum of terms that are independent in time, so the form of the final controller independently takes the minimum at each time step

𝑃𝑃𝐶𝐶𝑘𝑘 = argmin𝑃𝑃𝐶𝐶

𝐶𝐶𝑘𝑘𝑃𝑃𝐶𝐶𝑘𝑘 , 𝑆𝑆𝑆𝑆𝐶𝐶𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 + 𝜆𝜆𝑃𝑃𝐶𝐶𝑘𝑘 (6)

with 𝜆𝜆 as a constant. Of course, the full system model does not fully follow the listed assumptions 1-4, so for implementation in simulation and real-time the full model is used. The actual loss models are

𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙−𝐶𝐶 = 𝐼𝐼𝐶𝐶2𝑅𝑅𝐶𝐶 (7) 𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙−𝑏𝑏 = 𝐼𝐼𝑏𝑏2𝑅𝑅𝑏𝑏 (8) 𝑃𝑃𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙−𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑓𝑓(𝐼𝐼𝑏𝑏) (9)

The power commands are translated into currents using the battery and capacitor charge levels. The hardware takes current commands, so the algorithm implemented in real time considers the capacitor current 𝐼𝐼𝐶𝐶𝑘𝑘

𝐼𝐼𝐶𝐶𝑘𝑘 = argmin𝐼𝐼𝐶𝐶∈𝐼𝐼

𝐶𝐶𝑘𝑘𝐼𝐼𝐶𝐶𝑘𝑘 , 𝑆𝑆𝑆𝑆𝐶𝐶𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 , 𝑆𝑆𝑆𝑆𝐶𝐶𝑑𝑑𝑏𝑏𝑐𝑐 + 𝜆𝜆𝐼𝐼𝐶𝐶𝑘𝑘 (10)

where 𝐼𝐼 reflects the allowable currents based on the operating conditions. Many solution methods exist for this type of minimization, but multiple local minima often occur and gradient descent algorithms can fail. In real-time, the most reliable method is to calculate the value of several hundred possible commands and select the minimum of that finite list. The loss in accuracy is very small compared to the increased real-time performance.

Intuitively, the “equivalence” factor 𝜆𝜆 represents the cost of enforcing the constraint (3), in that the capacitor cannot provide energy in the long run and power must be drawn from the battery. Negative 𝐼𝐼𝐶𝐶 represents capacitor charging, and therefore more power drawn from the battery, so positive 𝜆𝜆 incentivizes this nominally undesirable choice. The process balances the desire to minimize losses with the long-term need to use battery energy. The effect is that the capacitor primarily handles the high-loss demands, leaving the battery to provide the average power.

This simple controller did not consider capacity limits on the capacitor. To discourage capacitor operation near the voltage limits and to leave a margin for upcoming events, an

© 2019 IEEE. Accepted Version. Published version at DOI: 10.1109/TIA.2019.2911057 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new

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Fig. 14 Controller solution for single time step and battery output power

command, demonstration of loss curve scaled via λ0 and β. Note the rightward shift to encourage output power.

offset adjustment is added to λ based on the Li-ion capacitor OCV’s deviation from the target, with scaling factor β

𝜆𝜆(𝑏𝑏) = 𝜆𝜆0 − 𝛽𝛽𝑉𝑉𝐶𝐶 − 𝑉𝑉𝐶𝐶−𝑏𝑏𝑏𝑏𝑡𝑡𝑡𝑡𝑡𝑡𝑏𝑏(𝑏𝑏). (11)

The target voltage is half way between the maximum Li-ion capacitor voltage, VC-max, and the battery open circuit voltage. The parameter λ is now a function of time rather than constant. As the capacitor value approaches its upper limit, 𝜆𝜆 decreases, encouraging capacitor discharge and battery charge. As the capacitor voltages gets low the opposite effect occurs. The effect of λ on the selection of the operating point is shown in Fig. 14.

The best choice for λ is dependent on the drive cycle and not known a priori for the real-time controller. Typical driving cycles are used to select a baseline value for 𝜆𝜆0 by using a branch and bound search to find a value that roughly maintains capacitor charge. The offset adjustment method (11) provides live corrections based on the type of driving by observing the capacitor voltage. For a system without capacitor capacity limits that follows the listed assumptions and a correct λ, the base method (10) can produce the same results as the DP method [15]. Typical drive cycles are also used in selecting 𝛽𝛽 to maintain the voltage deviations within reasonable limits.

B. Real-time controller tuning and modeled performance The real-time controller is tuned by varying parameters λ0

and β. A large λ0 value will penalize use of the Li-ion capacitor, causing the Li-ion capacitor to stay near full charge as shown in Fig. 15 (a). A large β value will force the Li-ion capacitor voltage to stay near the target value, as is also shown in Fig. 15 (a). Tuning parameter λ0 was chosen to be six because this resulted in the most increase in range for all all driving cases, as shown in Fig. 15 (b). Parameter β was likewise chosen to be 0.3 to achieve the greatest increase in range. For these tuning parameter values, the controller was found to achieve nearly as good of performance as the DP algorithm. The real-time controller achieved range increases of 4.9 to 20.1%, while DP achieved range increases of 5.2 to 21.1%, as shown in Fig. 15 (c). There were somewhat higher HESS losses with the real-time control, an increase of between 14 and 37% (Fig. 15 (c)), indicating an area future control systems could improve upon.

The performance of a rule-based controller was also modeled for comparison with the developed real-time controller. For the rule-based controller power was split evenly between the battery and Li-ion capacitor packs during

(a) Effect of tuning parameters λ0 and β on Li-ion capacitor voltage

(b) Improvement in range versus tuning parameter λ0 for β = 0

(c) Range improvements and total HESS loss for optimal DP control, real

time controller with λ0 =6 and β = 0.3, and rule based control

Fig. 15 Real time controller tuning and comparison to optimal DP control

discharges and the Li-ion capacitor pack was used to absorbed all of the charge power, keeping the Li-ion capacitor sufficiently charged. This simple controller performed fairly well as shown in Fig. 15 (c), but achieved less range and had higher losses than the proposed real-time controller for all but the US06 drive cycle where it performed similarly. This suggests it is worthwhile to develop a more sophisticated controller as is done here.

VI. EXPERIMENTAL VERIFICATION OF FULL SCALE HESS AND REAL TIME CONTROL SYSTEM

A. Experimental Setup

The entire HESS, as shown in Fig. 2 and Fig. 5, along with the real-time controller developed in section V, was tested as a system to verify the model accuracy and controller performance. The HESS was tested while installed in the vehicle and was connected via a set of power cabling to a high current, high power battery cycler. The battery cycling system, a D&V Electronics BST 240 unit, was used to draw a power profile for a standard drive cycle from the HESS. The HESS was controlled with a real-time control system installed in the vehicle, a dSPACE MicroAutoBox. As shown in Fig. 16, the controller utilizes the HESS input current, Li-ion capacitor current and voltage, and Li-ion battery current and voltage measurements to calculate the dc/dc converter lower side

© 2019 IEEE. Accepted Version. Published version at DOI: 10.1109/TIA.2019.2911057 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new

collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

(a) Experimental setup for testing HESS with real time controller

(b) Kalman filter for estimating Li-ion capacitor voltage

Fig. 16 Experiment setup and Kalman filter for testing HESS

current command. The real-time control algorithm also requires battery state of charge and Li-ion capacitor state of charge for calculation of the losses and of the control penalty for keeping the Li-ion capacitor voltage in the desired range. The battery state of charge is calculated via coulomb counting, while the Li-ion capacitor OCV, which is analogous to state of charge of the Li-ion capacitor, must be estimated with a Kalman filter because coulomb counting is not accurate enough. The real-time control algorithm was implemented as a series of mathematical calculations as described in section V. To reduce the computational load, the algorithm could instead be implemented as a look up table, with the HESS power command, battery SOC, and Li-ion capacitor SOC as inputs and the dc/dc converter current command as an output.

B. Kalman Filter for Estimation of Li-ion Capacitor OCV Coulomb counting is commonly used to estimate the SOC

of an energy storage device, but it requires a very accurate current sensor because any error will be integrated over time. The current sensors in the vehicle have offset and gain errors as high as 1% or a few amps. This is quite large when compared to the less than 2Ah capacity of Li-ion capacitor pack, necessitating the use of a Kalman filter. In a Li-ion capacitor, the stored energy is a function of capacitance and voltage. The capacitor’s OCV cannot be directly measured during operation while current is flowing since the cell ohmic resistance and the bus bar resistance effect the terminal voltage measurement. In [19], a Kalman filter (KF) is shown to have the capability to estimate the internal states of an energy storage system. According to the Li-ion capacitor model in Fig. 9 (b), the discrete-time state-space model is

𝑉𝑉𝐶𝐶𝑘𝑘+1 = 𝑉𝑉𝐶𝐶𝑘𝑘 +𝛥𝛥𝑏𝑏𝐶𝐶𝐼𝐼𝐶𝐶𝑘𝑘 (12)

𝑉𝑉𝐶𝐶−𝑙𝑙𝑜𝑜𝑏𝑏𝑘𝑘 = 𝑉𝑉𝐶𝐶𝑘𝑘 + 𝑅𝑅𝐶𝐶𝐼𝐼𝐶𝐶𝑘𝑘 (13)

where 𝑉𝑉𝐶𝐶𝑘𝑘 is the capacitor voltage, 𝑉𝑉𝐶𝐶−𝑙𝑙𝑜𝑜𝑏𝑏𝑘𝑘 is the measured terminal voltage, 𝐼𝐼𝐶𝐶𝑘𝑘 is the current flow into the Li-ion capacitor, 𝐶𝐶 is the capacitance, and 𝑅𝑅𝐶𝐶 is the resistance. The values of 𝐶𝐶 and 𝑅𝑅𝐶𝐶 are from the measurement in Fig. 8 (b). The algorithm of a KF for an energy storage system discussed in [19] was utilized in the control system. Due to the Li-ion capacitor model being a one-state system, the noise covariance matrices can be tuned using trial and error. The tuned values of Q and R in the KF are 1e-3 and 2. The diagram of the Kalman filter is shown in Fig. 16 (b).

C. Experimental Results for US06 Drive Cycle The HESS performance was tested for a US06 drive cycle,

the most aggressive and dynamic of the standard drive cycles. The measured power profile for the test, as shown in Fig. 17 (a) below, has regenerative braking power (positive) as high as 60kW and discharge power (negative) as high as 80kW. Due to limitations of the battery cycler, the US06 test had to be commanded as a current profile rather than a power profile, causing the power waveform to be slightly different than that in Fig. 12. Additionally the battery pack, which is about three years old, was found to have lost about 25% of its capacity, possibly due to the battery being kept at a low SOC. The battery capacity was adjusted accordingly in the model to account for this.

Overall, the experimental HESS functioned very well, providing 1500 seconds (32.2 km) of drive time and improving performance in several qualitative ways which can be observed Fig. 17 (a). Improvements include: (1) filtering and smoothing of the power provided by the battery, (2) splitting the system power between the battery and Li-ion capacitor, and

(a) Li-ion capacitor, battery, and

total HESS power (b) Li-ion capacitor measured voltage

and Kalman filter estimated OCV

(c) Battery and ultracapacitor voltage, measured and modeled

Fig. 17 Measured and modeled full scale HESS performance for a US06 drive cycle

© 2019 IEEE. Accepted Version. Published version at DOI: 10.1109/TIA.2019.2911057 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new

collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

(a) Battery, li-ion capacitor, and dcdc converter loss for US06 cycle, with

measured loss values calculated from measured current and model

(b) Battery charge consumed and battery and li-ion capacitor current Fig. 18 Measured full scale HESS performance characteristics versus

modeled performance

(3) capturing most of the regenerative braking power with the Li-ion capacitor. This performance was achieved in part due to the Kalman filter providing an accurate and reliable estimate of Li-ion capacitor OCV, as is shown in Fig. 17 (b). The modeled and measured voltages, shown in Fig. 17 (c), align fairly well when it is considered that a very small difference in average current drawn from the Li-ion capacitor pack (i.e. 1A) will result in a significant difference in voltage.

To provide a quantitative assessment of the performance of the HESS, the measured power for the experimental test was used as the input to the HESS model, and the model calculated performance was compared to the measured results as shown in Fig. 18. The total losses for the drive cycle were calculated (Fig. 18(a)), and losses of 950Wh were predicted for the battery only case, 552Wh for the HESS with optimal DP control, 650Wh for the modeled RT control, and 642Wh for the experimental RT control case. For the experimental case, losses were calculated from the measured currents and the presented models. The consumed battery amp-hours and battery and Li-ion capacitor rms currents were also calculated (Fig. 18(b)). For the modeled and experimental RT control cases the rms currents (Arms) were very similar (63 vs 62 Arms for the battery and 46 vs 47 Arms for the Li-ion capacitor), and importantly a similar amount of amp-hours (20.8 vs 21.3 Ah) were drawn from the battery, showing the consumed charge for the drive cycle was within 3% of predicted. Overall the results show excellent alignment, proving that the accuracy of the proposed modeling method and the performance of the developed real time control method.

VII. CONCLUSIONS A hybrid energy storage system capable of providing more

than 175kW, the peak electrical power draw of the plug-in hybrid powertrain, was developed. The hybrid energy storage

system was shown to enable the use of high energy density battery cells by pairing the battery with a higher power capability Li-ion capacitor pack. The optimal power split between the battery and Li-ion capacitor pack was calculated using dynamic programming for a range of drive cycles, and the HESS was shown to have the potential to substantially increase regenerative braking energy capture and to reduce battery and overall energy storage system losses. A real-time controller was developed which performs nearly as well as the optimal control solution, and it was tested on the full-scale HESS demonstrating the accuracy of the system modeling and the performance achievable in a real system. The developed HESS is shown to be a promising solution for high performance applications, and the concept could be applied to boost the power capability of any battery pack.

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collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

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BIOGRAPHIES

Phillip Kollmeyer (IEEE S’04-M’16) received the B.S.(2006), M.S.(2011), and Ph.D.(2015) degrees in electrical engineering from the University of Wisconsin-Madison, USA. As a graduate student, he built a prototype light-duty electric truck and led the development of a new energy storage test facility. He also performed a range of projects on hybrid energy storage, battery aging, and battery and ultracapacitor modeling, and received two awards for his teaching in the electric machines and drives area.

He is currently a Post-Doctoral fellow at McMaster University, Hamilton, ON, Canada, where his focus is energy storage and electric drivetrain research for transportation applications.

Mackenzie Wootton received the B.Sc degree in electrical engineering from Queen's University, Kingston, ON, Canada in 2016 and the M.A.Sc degree in electrical engineering from McMaster University, Hamilton, ON, Canada in 2018. He was part of the McMaster Engineering EcoCAR 3 Team from 2016-2018 and currently works on electric vehicle conversions for off-highway applications.

John Reimers (IEEE S'16) received the B.Eng. degree in electrical engineering from McMaster University, Hamilton, Ontario, Canada in 2016, where he is currently working toward the Ph.D. degree with the McMaster Institute for Automotive Research and Technology (MacAUTO). He previously led a student team in the development and implementation of a hybrid-electric powertrain for an advanced vehicle technology competition. His research interests include power electronics and

motor drives for electrified transportation applications. Daniel F. Opila (M’08) received the B.S. and M.S. degrees from the Massachusetts Institute of Technology, Cambridge, MA, USA, in 2002 and 2003, respectively, and the Ph.D. degree from the University of Michigan, Ann Arbor, MI, USA, in 2010. He is currently an Assistant Professor of electrical and computer engineering at the United States Naval Academy, Annapolis, MD, USA. He has previously worked in various engineering positions at GE Power Conversion, Ford Motor Company,

Orbital Sciences Corporation, and Bose Corporation. He specializes in optimal control of energy systems, including hybrid vehicles, naval power systems, power converters, and renewables.

Himesh Kurera is currently pursuing a B.Eng degree in Electrical Engineering from McMaster University, Hamilton, Ontario, Canada, and is expected to graduate in April of 2019. He was previously the Electrical Co-Lead for the McMaster EcoCAR 3 team and is currently working as a Research Assistant at the McMaster Automotive Resource Center (MARC).

Mrudang Kadakia is currently pursuing a B.Eng degree in Electrical Engineering from McMaster University, Hamilton, Ontario, Canada, and is expected to graduate in April of 2019. He was previously the Electrical Co-Lead for the McMaster EcoCAR 3 team and is currently working as a Research Assistant at the McMaster Automotive Resource Center (MARC). Ran Gu (S'15-M'16) received the B.S. degree in automation from Beijing Information Science & Technology University, Beijing, China, in 2010, the M.S. degree in electrical engineering from Illinois Institute of Technology (IIT), Chicago, Illinois, USA, in 2012, and the Ph.D. degree in electrical engineering from McMaster University, Hamilton, ON, Canada, in 2016. He is currently working as a battery engineer at Evelozcity. Before joining Evelozcity, he was working as a post-doctoral research

fellow (2016 - 2018) and research assistant (2012 - 2016) for the Canada Excellence Research Chair in Hybrid Powertrain Program, Hamilton, ON, Canada. His main research areas include high fidelity battery modeling, states estimation, and battery management system control strategy in electrified transportation systems.

Tyler Stiene received a B.Eng and Management degree in Mechatronics Engineering and M.A.Sc from the Department of Electrical & Computer Engineering at McMaster University, Hamilton Ontario Canada in 2014 and 2017 respectively. Tyler was a member of McMaster Formula Hybrid from 2011 to 2015 and Engineering Manager of the McMaster Engineering EcoCAR 3 team in 2015 and 2016. During Tyler's time with these teams he led the development of two hybrid vehicle's, winning numerous

awards including Best Engineered Hybrid three consecutive years. Tyler is now a Research Engineer at McMaster University developing software and simulation tools to support vehicle electrification development and research.

Ephrem Chemali (IEEE S’14-M’19) received the B.Sc. (Honours) and M.Sc. degrees in Physics from York University, Toronto, in 2009 and 2011, respectively. After completing his M.Sc., he worked as an engineering lead for Moose Power. From 2014 to 2018, Ephrem completed a PhD in Electrical and Computer Engineering; specializing in Machine Learning and Energy Management Systems at McMaster University. Ephrem is currently working as a Senior Machine Learning Engineer at

Huawei Technologies where he focuses on state-of-the-art Computer Vision algorithms, Meta-Learning, Neural Architecture Search or AutoML and AI Explainability and Attention. His primary research interests lie in Artificial Intelligence (AI), autonomous and electric vehicles.

Megan Wood is currently pursuing a M.A.Sc. in Electrical and Computer Engineering at McMaster University. Her passion for automotive engineering has made itself evident in her work with the McMaster's many vehicle teams. She has been a part of the McMaster Engineering EcoCAR Team for over 5 years now and is very proud of the work she has done in her role as engineering manager. She has been interested in automotive design since a young age and always knew she wanted to pursue a career in the

automotive industry.

Ali Emadi (IEEE S’98-M’00-SM’03-F’13) received the B.S. and M.S. degrees in electrical engineering with highest distinction from Sharif University of Technology, Tehran, Iran, in 1995 and 1997, respectively, and the Ph.D. degree in electrical engineering from Texas A&M University, College Station, TX, USA, in 2000. He is the Canada Excellence Research Chair Laureate at McMaster University in Hamilton, Ontario, Canada. He is also the holder of the NSERC/FCA Industrial Research Chair in Electrified

Powertrains and Tier I Canada Research Chair in Transportation Electrification and Smart Mobility. Before joining McMaster University, Dr. Emadi was the Harris Perlstein Endowed Chair Professor of Engineering and Director of the Electric Power and Power Electronics Center and Grainger Laboratories at Illinois Institute of Technology in Chicago. He was the advisor for the Formula Hybrid Teams at Illinois Tech and McMaster University, which won the GM Best Engineered Hybrid System Award at the 2010, 2013, and 2015 competitions. He is the principal author/coauthor of over 450 journal and conference papers as well as several books. Dr. Emadi was the Inaugural General Chair of the 2012 IEEE Transportation Electrification Conference and Expo (ITEC) and has chaired several IEEE and SAE conferences in the areas of vehicle power and propulsion. He is the founding Editor-in-Chief of the IEEE Transactions on Transportation Electrification.